The Science and Engineering of Materials (MindTap Course List)
7th Edition
ISBN: 9781305076761
Author: Donald R. Askeland, Wendelin J. Wright
Publisher: Cengage Learning
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Chapter 5, Problem 5.12P
To determine
To compare:-The rates of chemical relation at two different temperatures.
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A mechanism for hardening steel is called carburization. To achieve this process, the piece of steel is exposed to an atmosphere rich in hydrocarbon such as methane (CH4). Consider a steel with a carbide concentration of 0.25wt%, which must be treated at 950˚C. If the carbon concentration at the surface is suddenly increased to 1.20wt%, how long does it take for a penetration of 0.5mm from the surface to reach a concentration of 0.80wt%? . The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2s-1. Assume that the piece of steel is semi-finite. Use the table below.
Compare the diffusion coefficients (in cm²/s) of nitrogen in BCC and FCC iron at the allotropic transformation temperature of 912°C.
Decc
-153606
X
Your response differs from the correct answer by more than 10%. Double check your calculations, cm²/s
-1976-7
Dicc
x
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm2/s
Question 1Helium gas is contained in a cylinder by a gas-tight piston which can beassumed to move without friction. The gas occupies a volume of 1 x 10^-3m^3 temperature of 300K and a pressure of 1 x 10^5 Pa.(a) Calculate :i.the number of helium atoms in the container,ii.the total KE of the helium atoms(b) Energy is now supplied to the gas in such a way that the gas expands andthe temperature remains constant at 300K. State, and explain what changes, if any, will have occurred in the following quantities :i. The internal energy of the gasii. The root-mean-square speed of the helium atomsiii. The density of the gas.(Given : Boltzmann's constant = 1.38 x 10^23 JK^-1)
Chapter 5 Solutions
The Science and Engineering of Materials (MindTap Course List)
Ch. 5 - What is the driving force for diffusion?Ch. 5 - Give three examples of materials processes that...Ch. 5 - In the carburization treatment of steels, what are...Ch. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - A certain mechanical component is heat treated...Ch. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Compare the diffusion coefficients of carb on in...Ch. 5 - Prob. 5.18PCh. 5 - Activation energy is sometimes expressed as...Ch. 5 - Prob. 5.20PCh. 5 - The activation energy for the diffusion of copper...Ch. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Write down Fick’s first law of diffusion. Clearly...Ch. 5 - Prob. 5.27PCh. 5 - Prob. 5.28PCh. 5 - Prob. 5.29PCh. 5 - Prob. 5.30PCh. 5 - A 1-mm-thick BCC iron foil is used to separate a...Ch. 5 - Prob. 5.32PCh. 5 - Prob. 5.33PCh. 5 - A 0.001 in. BCC iron foil is used to separate a...Ch. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.37PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39PCh. 5 - Prob. 5.40PCh. 5 - Prob. 5.41PCh. 5 - Prob. 5.42PCh. 5 - Prob. 5.43PCh. 5 - Prob. 5.44PCh. 5 - Prob. 5.45PCh. 5 - Prob. 5.46PCh. 5 - Prob. 5.47PCh. 5 - Prob. 5.48PCh. 5 - Pure zinc is to be diffused into copper by dipping...Ch. 5 - Nitriding is a process in which nitrogen is...Ch. 5 - Determine the carburizing time necessary to...Ch. 5 - Prob. 5.52PCh. 5 - Prob. 5.53PCh. 5 - Prob. 5.54PCh. 5 - Prob. 5.55PCh. 5 - Prob. 5.56PCh. 5 - Prob. 5.57PCh. 5 - Prob. 5.58PCh. 5 - Compare the rate at which oxygen ions diffuse in...Ch. 5 - Prob. 5.60PCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - Prob. 5.63PCh. 5 - Prob. 5.64PCh. 5 - Prob. 5.65PCh. 5 - A 0.80% C steel must operate at 950°C in an...Ch. 5 - Prob. 5.67PCh. 5 - Prob. 5.68PCh. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - Prob. 5.71PCh. 5 - Prob. 5.72PCh. 5 - Most metals and alloys can be processed using the...Ch. 5 - Prob. 5.74PCh. 5 - Prob. 5.75PCh. 5 - Prob. 5.76PCh. 5 - A ceramic part made from MgO is sintered...Ch. 5 - Prob. 5.78PCh. 5 - What are the advantages of using hot pressing and...Ch. 5 - Prob. 5.80PCh. 5 - Prob. 5.81DPCh. 5 - Design a spherical tank, with a will thickness of...Ch. 5 - Prob. 5.83DPCh. 5 - Prob. 5.84DPCh. 5 - Prob. 5.85DPCh. 5 - Prob. 5.86CPCh. 5 - Prob. 5.87CPCh. 5 - Prob. 5.88CPCh. 5 - Prob. 5.1KP
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- A diffusion couple of two metals, A and B, was fashioned as shown in Figure 5.1. After a 26 hour heat treatment at 1170°C (and subsequent cooling to room temperature) the concentration of A is 4.0 wt% at the 11-mm position within metal B. If another heat treatment is conducted on an identical diffusion couple, only at 701°C for 26 hours, at what position (in mm) will the composition be 4.0 wt% A? The preexponential and activation energy values for the diffusion of A in B are 2.4 x 10-4 m²/s and 154 kJ/mol, respectively. i mmarrow_forwardRank the magnitudes of the diffusion coefficients from greatest to least for the following systems: N in Fe at 700°C Cr in Fe at 700°C N in Fe at 900°C Cr in Fe at 900°C Now justify this ranking. (Note: Both Fe and Cr have the BCC crystal structure, and the atomic radii for Fe, Cr, and N are 0.124, 0.125, and 0.065 nm, respectively. You may also want to refer to Section 5.4.)arrow_forwardDiffusion of carbon into the surface of BCC steel at 600oC for 10 hours results in a carbon concentration of 0.2wt% at a depth of 1.5 mm below the surface. At what depth will the same concentration be obtained if the diffusion time is increased to 20 hours, leaving the temperature at 600oarrow_forward
- A plate of iron is exposed to a carburizing atmosphere on one side and a decarburizing atmosphere on the other side at 850 oC. If a condition of steady state is achieved, calculate the diffusion flux of carbon through the plate if the concentrations of carbon at positions of 5 and 10 mm beneath the carburizing surface are 1.4 and 0.8 kg/m3, respectively. Assume a diffusion coefficient of 3 x 10 -11 m2/s at this temperature.arrow_forwardFind the diffusitivity of air in methane and the molecular diffusion of methane, if the tank filled with a mixture of methane and air at 102 kPa and 25 ⁰C is connected to another large tank filled with a different composition of methane and air also at 102 kPa and 25 ⁰C. The connection between the tanks is a tube with an inner diameter of 50 mm and length of 150 mm. The concentration of methane in one tank is 90% by mole and in the other, 5% by mole.arrow_forward3. A BCC iron alloy containing 0.05 wt% C is carburized at 1050°C such that the carbon concentration is 0.5 wt% at a distance 2mm from the surface. Meanwhile, the carbon concentration at the surface is kept constant at 1.5 wt% C. a. What is the value of the diffusion constant for carbon diffusing into BCC Fe at 1050 °C? Show all work. Write the relevant equation for the diffusivity within this box: Write the values of all of the parameters in the equation above within the box below: Write your final answer for the diffusivity within this box: b. Determine the diffusion time required to achieve the carbon profile described above. Show all work. Write the relevant equation needed to solve this problem within this box: Write the values of all of the given parameters in the equation above within the box below: Write the value for erf(z) within this box:arrow_forward
- The figure below shows five different steady-state concentration profiles from five separate tests, which had the same gas across identical membranes at the same temperature. Rank the diffusion flux of the five concentration profiles from lowest to highest. Using bullet points explain your answer. C(x)' (a) (b) (c) (d) (e) Membrane Thicknessarrow_forwardYou want to carburize a steel drill bit in the presence of methane. The drill bit initially has a uniform carbon concentration of 0.25 wt% and is to be treated at 950 oC (1750 oF). If the concentration of carbon at the surface is suddenly brought to and maintained at 1.20 wt%, how long will it take to achieve a carbon content of 0.80 wt% at a position 0.5mm below the surface? (The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2/s.)arrow_forwardConsider an alloy that is undergoing carburizing process, initially has a uniform carbon concentration of 0.27 wt% and is to be treated at 950°C (1750°F). If the concentration of carbon at the surface is suddenly brought to and maintained at 1.32 (c) wt%, how long will it take to achieve a carbon content of 0.85% at a position 0.7 mm below the surface? The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2/s; assume that the steel piece is semi-finite.arrow_forward
- Nitrogen from a gaseous phase is to be diffused into pure iron at 700°C. If the surface concentration is maintained at 0.14 wt% N, what will be the concentration (in weight percent) 2.3 mm from the surface after 6.5 h? The diffusion coefficient for nitrogen in iron at 700°C is 1.4 x 10-10 m²/s. Z 0.00 0.025 0.0282 0.60 0.05 0.0564 0.30 erf(z) 0.0000 0.55 0.35 Z erf(z) 0.40 0.45 0.50 0.65 0.10 0.1125 0.70 0.6778 1.6 0.5633 1.3 0.6039 0.4755 1.1 Z 0.15 0.1680 0.75 0.7112 0.20 0.2227 0.80 0.7421 1.8 0.25 0.2763 0.85 0.7707 1.9 0.9928 0.3286 0.90 0.7970 0.5205 1.2 0.6420 1.5 1.4 0.3794 0.95 0.8209 2.2 0.4284 1.0 1.7 0.9103 2.0 erf(z) 0.9340 0.9523 0.9661 2.8 0.9763 0.9838 0.9891 0.9953 0.8427 2.4 0.9993 0.9981 0.8802 2.6 0.9998 0.9999arrow_forwardWhat is degree of reaction? Give expressions of reaction rate equations by degree of reaction.arrow_forwardThe running engine of an automobile produces carbon monoxide (CO), a toxic gas, at the rate of about 188 g CO per hour. A car is left idling in a poorly ventilated garage that is 6.0 m long,4.0 m wide, and 2.2 m high at 20°C. (a) Calculate the rate of CO production in mol/min. (b)How long would it take to build up a lethal concentration of CO of 1000 ppmv (parts per millionby volume)? Round off to 4 sig. figures for all calculations made prior to final answer and the final answer should be in 3 sig. figuresarrow_forward
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